Questions on the document
- East West Distributing is in the process of trying to determine where they should schedule next year’s production of a popular line of kitchen utensils that they distribute. Manufacturers in four different countries have submitted bids to East West. However, a pending trade bill in Congress will greatly affect the cost to East West due to proposed tariffs, favorable trading status, etc.
- A manufacturing company is considering expanding its production capacity to meet a growing demand for its product line of air fresheners. The alternatives are to build a new plant, expand the old plant, or do nothing. The marketing department estimates a 35 percent probability of a market upturn, a 40 percent probability of a stable market, and a 25 percent probability of a market downturn. Georgia Swain, the firm’s capital appropriations analyst, estimates the following annual returns for these alternatives:
- A calculus instructor uses computer aided instruction and allows students to take the midterm exam as many times as needed until a passing grade is obtained. Following is a record of the number of students in a class of 20 who took the test each number of times.
After careful analysis, East West has determined the following cost breakdown for the four manufacturers (in $1,000’s) based on whether or not the trade bill passes:
|
Bill Passes |
Bill Fails |
|
|
Country A |
260 |
210 |
|
Country B |
320 |
160 |
|
Country C |
240 |
240 |
|
Country D |
275 |
210 |
|
a. |
If East West estimates that there is a 40% chance of the bill passing, which country should they choose for manufacturing? |
|
b. |
Over what range of values for the “bill passing” will the solution in part (a) remain optimal? |
|
Market Upturn |
Stable Market |
Market Downturn |
|
|
Build new plant |
$690,000 |
$(130,000) |
$(150,000) |
|
Expand old plant |
490,000 |
(45,000) |
(65,000) |
|
Do nothing |
50,000 |
0 |
(20,000) |
a. What should the company do?
b. What returns will accrue to the company if your recommendation is followed?
(I created the table below)
. Decision tree:
|
Students |
Number of Tests |
|
10 |
1 |
|
7 |
2 |
|
2 |
3 |
|
1 |
4 |
|
a. |
Use the relative frequency approach to construct a probability distribution and show that it satisfies the required condition. |
|
b. |
Find the expected value of the number of tests taken. |
|
c. |
Compute the variance. |
|
d. |
Compute the standard deviation. |
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